Electromagnetic units of measure
In physics many are unit systems for electrical and magnetic quantities have been developed. The SI has prevailed for the most part; At least in theoretical physics, however, some authors prefer the Gaussian variant of the CGS system.
Not only the specific selection, but also the number of basic quantities in a physical system of units is arbitrary: One can eliminate basic quantities from a unit system by choosing instead the proportionality factor in a linear “law of nature” as a dimensionless number. In theoretical atomic and particle physics, for example, one works with a system of units that has a single base quantity, since vacuum, the speed of light and Planck's quantum of action are set equal to 1.
Electromagnetic quantities are linked to mechanical quantities by several linear laws. The following relationships are particularly relevant for the choice of the unit system:
The Coulomb law , which gives the force F between two point charges Q 1 and Q 2 at a distance r ,
the Ampère force law , the force F between two currents I 1 and I 2 -carrying conductors of the length L in the distance d indicates
This leaves two independent proportionality constants and , which allow an arbitrary choice of an electrical and a magnetic base unit. In systems of measurement that explicitly reduce the electromagnetic quantities to mechanical quantities, one can choose both constants as dimensionless numbers or as mechanical quantities of arbitrary dimensions.
Electrostatic system of units
The Electrostatic System of Units (abbreviated esu , or ESU for e lectro s tatic u nits ) is the former way, that is ; so is .
Electromagnetic system of units
The Electromagnetic System of Units (abbreviated emu , or EMU for e lectro m agnetic u nits ) sets ; so is .
Gaussian system of units
Heaviside-Lorentz unit system
The Heaviside-Lorentz system of units also chooses , but differs from the Gaussian system in the choice . The factor 4π anticipates an integration over the solid angle; it makes Coulomb's law more complicated, but simplifies the calculation of the capacitance of a plate capacitor.
International system of units
The International System of Units (SI) has an additional base unit, the ampere . This results in a further constant, the magnetic field constant , as well as the electrical field constant linked to it . The SI sets , and .
Before the change in the SI system of units in 2019 , the ampere was defined by the Amperes law of force . Therefore the magnetic field constant had an exact value , and since the definition of the meter is specified, it also had an exact value. With the current definition of the ampere, and are measured quantities with measurement uncertainty.
The following table gives an overview of the form of the most important equations in electrodynamics in the various systems of units:
|theme||formula||Constant K (or , ) in the following system of units:
Force effect of
Electromagnetic units in different systems
|unit||Gaussian unit in cgs|
|charge||Q||1 C||≙||10 −1 c||statC||10 −1||ABC||10 −1 c||Fr.||Fr = statC =||g 1/2 cm 3/2 s −1|
|Amperage||I.||1 A||≙||10 −1 c||statA||10 −1||abA||10 −1 c||statA||statA =||g 1/2 cm 3/2 s −2|
|tension||U||1 V||≙||10 8 c −1||statV||10 8||abV||10 8 c −1||statV||statV =||g 1/2 cm 1/2 s −1|
|electric field strength||E.||1 V / m||≙||10 6 c −1||statV / cm||10 6||abV / cm||10 6 c −1||statV / cm||statV / cm =||g 1/2 cm −1/2 s −1|
|electric dipole moment||p||1 C · m||≙||10 1 c||statC · cm||10 1||abC cm||10 19 c||D.||D =||g 1/2 cm 5/2 s −1|
|magnetic flux density||B.||1 T||≙||10 4 c −1||instead of||10 4||G||10 4||G||G =||g 1/2 cm −1/2 s −1|
|magnetic field strength||H||1 A / m||≙||4π · 10 −3 c||statA / cm||4π · 10 −3||Oe||4π · 10 −3||Oe||Oe =||g 1/2 cm −1/2 s −1|
|magnetic dipole moment||m, μ||1 A · m 2||≙||10 3 c||statA cm 2||10 3||abA cm 2||10 3||erg / G||G =||g 1/2 cm 5/2 s −1|
|magnetic flooding||Θ||1 A||≙||4π · 10 −1 c||statA||4π · 10 −1||abA||4π · 10 −1||Gb||Gb =||g 1/2 cm 1/2 s −1|
|magnetic river||Φ||1 Wb||≙||10 8 c −1||statT cm 2||10 8||G cm 2||10 8||Mx||Mx =||g 1/2 cm 3/2 s −1|
|resistance||R.||1 Ω||≙||10 9 c −2||s / cm||10 9||abΩ||10 9 c −2||s / cm||cm −1 s|
|specific resistance||ρ||1 Ω · m||≙||10 11 c −2||s||10 11||abΩ cm||10 11 c −2||s||s|
|capacity||C.||1 F.||≙||10 −9 c 2||cm||10 −9||abF||10 −9 c 2||cm||cm|
|Inductance||L.||1 H.||≙||10 9 c −2||cm −1 s 2||10 9||fromH||10 9 c −2||cm −1 s 2||cm −1 s 2|
|electrical power||P||1 V * A = 1 W||=||10 7||erg / s||10 7||erg / s||10 7||erg / s||erg / s =||g cm 2 s −3|
The "≙" symbol indicates that this is not a simple conversion of units of measure. The CGS sizes generally have a different dimension than the corresponding size in the SI . That is why it is usually not allowed to simply replace the units in formulas. c is the speed of light .
- John David Jackson: Classical Electrodynamics. Appendix on Units and Dimensions (also published in German under the title Classical Electrodynamics ).
- Unit Systems in Electromagnetism - Guide from the University of Surrey